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Finance and Stochastics

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30-05-2017

The space of outcomes of semi-static trading strategies need not be closed

Authors: Beatrice Acciaio, Martin Larsson, Walter Schachermayer

Published in: Finance and Stochastics | Issue 3/2017

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Abstract

Semi-static trading strategies make frequent appearances in mathematical finance, where dynamic trading in a liquid asset is combined with static buy-and-hold positions in options on that asset. We show that the space of outcomes of such strategies can have very poor closure properties when all European options for a fixed date \(T\) are available for static trading. This causes problems for optimal investment, and stands in sharp contrast to the purely dynamic case classically considered in mathematical finance.

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Title: The space of outcomes of semi-static trading strategies need not be closed
Authors: Beatrice Acciaio
Martin Larsson
Walter Schachermayer
Publication date: 30-05-2017
Publisher: Springer Berlin Heidelberg
Published in: Finance and Stochastics / Issue 3/2017
Print ISSN: 0949-2984
Electronic ISSN: 1432-1122
DOI: https://doi.org/10.1007/s00780-017-0329-3

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